15
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This question is somewhat two-fold. I am in the process of creating a high-level Barbarian and am trying to determine if it makes more sense to take use dual weapons and capitalize on the additional damage that rage deals versus using great weapons, which benefit more from crits.

The Barbarian's primal path is Zealot, so he has a revolving door with death. For the purposes of race, we are taking advantage of the revolving door and using the Reincarnate spell liberally. From our Session 0, the character has died and been reincarnated 3 times and is currently a human. I've encouraged the DM to kill this character whenever he wants and we'll reincarnate him as something else. To simplify the complexities of changing race constantly, we are using the following house rules for reincarnation:

  • Retain your original race's stat bonuses, you lose all the other features.
  • Gain the features of your new race, but none of the stat bonuses.

Currently, the character is a human, but his original incarnation was half-elf. Due to the everchanging nature of his race, assume for the purposes of assessing this, that racial features that improve damage, like Savage Attacks, aren't applicable since the character could get Worfed at anytime.

The following assumptions should be considered:

  • The character does NOT have the the Dual Wielder feat.
  • The character does NOT have the Great Weapon Master feat.
  • If dual wielding, the character would use a weapon that dealt 1d6 in the main hand and 1d6 in the off-hand (I don't believe there are any light weapons capable of dealing more than 1d6 damage).
  • Character has 18 Strength.
  • For the purposes of damage calculation, assume the character is raging.
  • No multi-classing.
  • Almost always fighting recklessly for Advantage.
  • Assume the character's race is not one that provides a bonus to damage or critical damage (like half-orcs)
  • Do not account for plusses due to magic weapons.
  • ASIs are used in a manner that doesn't increase damage. For example, on boosting Con or Dex. Or on feats that don't increase damage.
  • Strength adjustments at level 20 should be considered since it is a class feature.

With those assumptions in mind, can someone advise me on which fighting style, on average, deals more damage per round considering the damage bonuses from the Barbarian class features? If the damage optimization changes, at what levels does that occur?

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    \$\begingroup\$ Will this character ever be a small race? Small creatures and heavy weapons don't mix well. \$\endgroup\$ – Derek Stucki Sep 11 '17 at 21:08
21
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Frame challenge: both.

As can be seen in the other answers, the difference in damage output is relatively small in a vacuum. However, combat in D&D rarely takes place in a vacuum (and if it does, your bigger concern would probably be breathing). I see nothing in your situation that gives you a reason to permanently choose one or the other. I suggest you carry both. The various situations likely to be encountered by your barbarian will create more of a difference in your ability to kill foes than exists between the two styles in a vacuum.

Therefore, I suggest that the better question for your explained situation is under what situations should my barbarian use one style or the other?

Two weapon fighting is probably better if:

  • You are currently a small race. Disadvantage with heavy weapons makes them far less effective.

  • Low hit point enemies. If they die in one hit from either, killing three per round is far better than killing two per round.

  • The combat is likely to last a long time.

  • Damaging more than one enemy is desirable, such as attacking trolls with flaming weapons.

Great weapons are better if:

  • The combat is short, but you still want to rage, due to losing a bonus action attack the first round with two weapon fighting.

  • Bigger hits are desirable, such as against zombies.

  • You can obtain exactly one magical weapon for your character (perhaps one ally can cast the magic weapon spell) when fighting enemies with resistance or immunity to non-magical weapons.

  • You are currently a half-orc. (You said to ignore this, but this answer is a frame challenge.)

  • Your opponent has a very high AC, as a greater percentage of hits will be crits, thus favoring the larger die.

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2
  • \$\begingroup\$ How did I miss this answer? Arrggh. I needed it for a link to an answer I wrote the other day. I really like your approach here. And, it's linked. Thank you, two years too late. \$\endgroup\$ – KorvinStarmast Aug 8 '19 at 14:29
  • 2
    \$\begingroup\$ "You are currently a half-orc". I love the phrasing. \$\endgroup\$ – leinaD_natipaC Nov 26 '19 at 15:40
20
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Dual wield

2 main hand attacks + 1 off-hand attack = 2*(d6+7)+(d6+3), expected value = 27.5

Expected number of criticals is 0.2925 a turn, with +3d6 (ev.=10.5) damage, +3.07 overall.

Two-handed

Assuming you use a greatsword or maul: 2 attacks = 2*(2d6+7), expected value = 28

Expected number of criticals is 0.195 a turn, with +3d6 (ev.=10.5) damage, +2.05 overall.

Assuming you use a greataxe: 2 attacks = 2*(d12+7), expected value = 27

Expected number of criticals is 0.195 a turn, with +3d12 (ev.=19.5) damage, +3.8 overall.

On later levels

On level 16 and 17 you get another Brutal die and +1 to rage damage. On level 20, you get +2 to your STR modifier. Accounting for this and adding in criticals directly:

\begin{array}{|c|c|} \hline & lv13 & lv17 & lv20\\ \hline 2x\ light& 30.57 & 34.59 & 38.59 \\ \hline g.sword & 30.05 & 32.73 & 36.73\\ \hline g.axe & 30.80 & 34.07 & 38.07\\ \hline \end{array}

So the damage starts similar, but starts to lean towards dual wielding at the end because of the big flat modifiers. But using two weapons will consume your bonus action too. Meaning you cannot use an off-hand attack on the turn you enter your rage. Also, if you are not completely ready for a fight you will need to draw both weapons to get this output. So you will lose an attack on the first turn of any fight. That is 13.5 damage + criticals on level 20. For the 0.52 difference in dmg/turn to balance this out you need to attack for over 26 turns after the first one. A battle this long is quite unlikely. For these reasons I am of the opinion that using a greataxe will be better.

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  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$ – V2Blast Aug 2 '19 at 5:19
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This does not address miss chances and assumes all attacks hit. Basic calcs are as follows:

  • Crit chance for a single attack with advantage is: 1-[(1-0.05)*(1-0.05)]=0.0975; therefore 9.75% chance.
  • Iterative attacks have a crit chance of: 1-[(1-0.0975)*(1-0.0975)...]
  • Therefore, 2 attacks have an 18.55% chance; 3 attacks have 26.5% chance.
  • Average die damage from a d6 weapon is 3.5.
  • Average die damage from a 2d6 weapon is 7.0.
  • Average die damage from a d12 weapon is 6.5.

tl;dr table:

\begin{array}{|c|c|} \hline & lv2 & lv5 & lv9 & lv13 & lv16 & lv17 & lv20\\ \hline 2x\ light& 15.65 & 25.43 & 29.36 & 30.28 & 33.28 & 34.21 & 38.21 \\ \hline g.sword & 13.34 & 27.30 & 29.30 & 29.95 & 31.95 & 32.60 & 36.60\\ \hline g.axe & 13.13 & 26.21 & 29.41 & 30.62 & 32.62 & 33.82 & 37.82\\ \hline \end{array}

It looks like the only notable turn away from dual wielding occurs at level 5, before Rage damage increases at level 9 cause dual wielding to pretty much run away with things. I found it also interesting that the great axe begins to outshine the great sword fairly early on, which is contrary to conventional wisdom and it manages to pull ahead dual-wielding for a bit at 13th level.

Level 2

  • Rage Damage +2
  • Advantage on all attack rolls

Dual Wielding

  • First Attack: 1d6+6=9.5 dmg
  • Second Attack: 1d6+2=5.5 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 0.65 damage per round (DPR)
  • Overall DPR: 15.65 dmg

Great Weapons

Great Sword:

First attack:

  • 2d6+6=13.0 dmg
  • Crit chance for 1 attack: 9.75%; therefore additional damage is 0.34 DPR
  • Overall DPR: 13.34 dmg

Great Axe:

  • First attack: 1d12+6=12.5 dmg
  • Crit chance for 1 attack: 9.75%; therefore additional damage is 0.63 DPR
  • Overall DPR: 13.13 dmg

Level 5

  • Rage damage +2
  • Extra attack feature gained

Dual Wielding

  • First Attack: 1d6+6=9.5 dmg
  • Second Attack: 1d6+6=9.5 dmg
  • Third Attack: 1d6+2=5.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 0.93 DPR
  • Overall DPR: 25.43 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+6=13.0 dmg
  • Second attack: 2d6+6=13.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 1.30 DPR
  • Overall DPR: 27.30 dmg

Great Axe:

  • First attack: 1d12+6=12.5 dmg
  • Second attack: 1d12+6=12.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 1.21 DPR
  • Overall DPR: 26.21 dmg

Level 9

  • Rage damage +3
  • Extra attack
  • Brutal critical (1 die)

Dual Wielding

  • First Attack: 1d6+7=10.5 dmg
  • Second Attack: 1d6+7=10.5 dmg
  • Third Attack: 1d6+3=6.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 1.86 DPR
  • Overall DPR: 29.36 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+7=14.0 dmg
  • Second attack: 2d6+7=14.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 1.30 DPR
  • Overall DPR: 29.30 dmg

Great Axe:

  • First attack: 1d12+7=13.5 dmg
  • Second attack: 1d12+7=13.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 2.41 DPR
  • Overall DPR: 29.41 dmg

Level 13

  • Rage damage +3
  • Extra attack
  • Brutal critical (2 dice)

Dual Wielding

  • First Attack: 1d6+7=10.5 dmg
  • Second Attack: 1d6+7=10.5 dmg
  • Third Attack: 1d6+3=6.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 2.78 DPR
  • Overall DPR: 30.28 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+7=14.0 dmg
  • Second attack: 2d6+7=14.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 1.95 DPR
  • Overall DPR: 29.95 dmg

Great Axe:

  • First attack: 1d12+7=13.5 dmg
  • Second attack: 1d12+7=13.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 3.62 DPR
  • Overall DPR: 30.62 dmg

Level 16

  • Rage damage +4
  • Extra attack
  • Brutal critical (2 dice)

Dual Wielding

  • First Attack: 1d6+8=11.5 dmg
  • Second Attack: 1d6+8=11.5 dmg
  • Third Attack: 1d6+4=7.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 2.78 DPR
  • Overall DPR: 33.28 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+8=15.0 dmg
  • Second attack: 2d6+8=15.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 1.95 DPR
  • Overall DPR: 31.95 dmg

Great Axe:

  • First attack: 1d12+8=14.5 dmg
  • Second attack: 1d12+8=14.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 3.62 DPR
  • Overall DPR: 32.62 dmg

Level 17

  • Rage damage +4
  • Extra attack
  • Brutal critical (3 dice)

Dual Wielding

  • First Attack: 1d6+8=11.5 dmg
  • Second Attack: 1d6+8=11.5 dmg
  • Third Attack: 1d6+4=7.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 3.71 DPR
  • Overall DPR: 34.21 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+8=15.0 dmg
  • Second attack: 2d6+8=15.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 2.60 DPR
  • Overall DPR: 32.60 dmg

Great Axe:

  • First attack: 1d12+8=14.5 dmg
  • Second attack: 1d12+8=14.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 4.82 DPR
  • Overall DPR: 33.82 dmg

Level 20

  • Rage damage +4
  • Extra attack
  • Brutal critical (3 dice)
  • Increase Strength by 4

Dual Wielding

  • First Attack: 1d6+10=13.5 dmg
  • Second Attack: 1d6+10=13.5 dmg
  • Third Attack: 1d6+4=7.5 dmg
  • Crit chance for 3 attacks: 26.50%; therefore additional damage is 3.71 DPR
  • Overall DPR: 38.21 dmg

Great Weapons

Great Sword:

  • First attack: 2d6+10=17.0 dmg
  • Second attack: 2d6+10=17.0 dmg
  • Crit chance for 2 attacks: 18.55%; therefore additional damage is 2.60 DPR
  • Overall DPR: 36.60 dmg

Great Axe:

  • First attack: 1d12+10=16.5 dmg
  • Second attack: 1d12+10=16.5 dmg
  • Crit chance for 1 attack: 18.55%; therefore additional damage is 4.82 DPR
  • Overall DPR: 37.82 dmg
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  • \$\begingroup\$ You list G.axe doing less damage on level 13 than on L9 \$\endgroup\$ – András Sep 11 '17 at 17:10
  • \$\begingroup\$ You do not take into account that you can crit multiple times in a turn. You list the chance to score at least one crit. \$\endgroup\$ – Szega Sep 16 '17 at 17:55
  • \$\begingroup\$ @Szega You'll have to elaborate, because I believe I did account for that. The chance to crit was evaluated based upon the chance for each attack. The crit chance for a round with 1 attack was compared to rounds that have 2 and 3 attacks and the odds of a successful crit increases accordingly. While it's possible for any round to have multiple crits, which would increase that single round's damage, there can also be rounds without any crits and thus providing 0 additional damage, which evens things out to provide the stated averages. \$\endgroup\$ – Pyrotechnical Sep 18 '17 at 16:32
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    \$\begingroup\$ I understand that the original character does not have the Great Weapon Master feat, however in the interest of a full comparison, I believe it would be interesting to see the gap; +10 damage / hit is rather brutal. It is not quite clear how to model the penalty (-5 AR), since hitting was not modeled here. \$\endgroup\$ – Matthieu M. Apr 14 '19 at 12:28
  • \$\begingroup\$ @Matthieu - I don’t know if that is beyond the scope of this question. It might qualify as its own standalone question. \$\endgroup\$ – EngrStudent Jan 6 at 12:07
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Is it okay for me to say that this brings out my inner math nerd? It does.

Disclaimers/Notes:
Note: The code below is in the “R” language. It is free, open source, primarily developed by masters and PhD’s in stats, and runs on all the operating systems. I like to use RStudio as the development environment, it is also free.

Also note that I learned on basic/advanced/expert D&D in the late 1980's, and am not yet up to speed on the details of 5th edition, thus I follow and study. To figure parts of this out, like proficiency bonus, I made a barbarian character on D&D beyond, with strength 18, and all other stats at 11. I had hoped it wouldn't bork the numbers up, but hope is not a guarantee. It looks like there is a +6 to hit because when I click roll it gives me a d20+6 to hit.

enter image description here

As a third note, I intend to make a summary section with a nice table, when I am done, and put it at the bottom. Thank you for being patient. Hopefully this will be a useful answer.

The previous answers do 98% of the job, so this is only about 2%. Seriously, check out the answers by Pyrotechnical and Derek first.

Starting in on the answer:
There are many breeds of average, and some are more meaningful than others depending on the context. Several versions include: arithmetic (classic), geometric, harmonic, power and censored (truncated, winsorized). Wikipedia There are many (many many) ways to skin this cat.

The context here is that the character is going into battle, and the player wants to maximize the expected damage and indicate transitions in that, depending on the style of weapon use for a barbarian.

Now I like to look at the 95% confidence interval instead of the mean. This gives me a 19 in 20 chance (in general) of reality overlapping my predicted region which is not bad odds.

I take into account:

  • First Attack: 1d6
  • Second Attack: 1d6
  • Crit hit on a 20
  • a basic enemy, the AC is 15 for goblin
  • a strength of 18 (+4 to damage, after dice rolls)
  • proficiency bonus to attack (+6) <-- this might be incorrect
  • when rolling a crit, the damage bonus is added only once per hit, after the dice are summed.

I use this R code:

#libraries
library(ggplot2)
library(dplyr)
library(psych)

#parameters

#how many repeats
n_tries <- 1e5

#parameters
target_ac <- 16
weapon_dmg <- 6
to_hit_mod <- 6
to_dmg_mod <- 4

weapon <- "dual"

log <- data.frame(dmg=numeric(length=n_tries), 
                  hit = numeric(length=n_tries))

for(i in 1:n_tries){
  
  # if(weapon == "dual"){
    rolls <- sample(1:20, 2, replace=T)
    dmg   <- sample(1:6, 2, replace=T) 
    dmg2  <- sample(1:6, 2, replace=T) 
  # } else {
  #   rolls <- sample(1:20, 1, replace=T)
  #   dmg   <- sample(1:6, 2, replace=T) %>% sum()
  #   dmg2  <- sample(1:6, 2, replace=T) %>% sum()
  # }
  to_hit <- 0
  for(j in 1:length(rolls)){
    #miss
    if(rolls[j] + to_hit_mod < target_ac){
      dmg[j] <- 0
      to_hit <- to_hit +1
    } 
    
    #crit
    if(rolls[j]==20){
      dmg[j] <- dmg[j] + dmg2[j]
    }
    
    #add damage bonus
    if(dmg[j]>0 & j==1){
      dmg[j] <- dmg[j] + to_dmg_mod
    }
  }
  
  log$dmg[i]<- sum(dmg)
  log$hit[i] <- to_hit > 0 
  
  
}

log$hit <- as.factor(log$hit)

ggplot(log, aes(x=dmg, fill=dmg>0)) + geom_histogram(binwidth = 1) +
  xlab("Damage per hit") + 
  ggtitle(weapon)


idx1 <- which(log$dmg >0)

print(summary(log[,1])) #all 
print(summary(log[idx1,1])) #given a hit
print(quantile(log[,1], c(0.025,0.5, 0.975)))
summary(log$hit)

And I get this distribution: enter image description here

Here are my summary stats:

> print(summary(log[,1])) #all 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   2.000   6.000   6.411  10.000  28.000 

> print(summary(log[idx1,1])) #given a hit
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.000   5.000   8.000   8.042  11.000  28.000 

> print(quantile(log[,1], c(0.025,0.5, 0.975)))
 2.5%   50% 97.5% 
    0     6    16 

> summary(log$hit)
    0     1 
30347 69653 

Which means my 95% confidence interval for damage is between 0 and 16, and my median damage per round is 6, while my mean per round is 6.411. It looks like only about 1/3 of rounds have no hit.

If I adjust for a single hit with a greatsword, I get the following plot: enter image description here

I get the following summary stats

> print(summary(log[,1])) #all 
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.000   8.000   6.383  12.000  28.000 

> print(summary(log[idx1,1])) #given a hit
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   6.00    9.00   11.00   11.61   13.00   28.00 

> print(quantile(log[,1], c(0.025,0.5, 0.975)))
 2.5%   50% 97.5% 
    0     8    18 

> summary(log$hit)
    0     1 
54967 45033 

This says that a greatsword gives mean of 6.383, and fails to hit more than it hits. I ran this for one hundred thousand times, so the uncertainty in the mean is likely smaller than the second decimal place.

When I compare this vs. Pyrotechnical the damage per round is very different, primarily because of accounting for AC.

Next steps (work in progress):

  • make 3 cases: dual, greatsword, greataxe
  • look at levels: 1, 2, 5, 9, 13, 16, 17, 20
  • find "weak", "average" and "strong" monster AC's and see if the ideal set changes
  • try pulling in the bounds, so something like 50% CI instead of 95%
  • think about encounters, so how many goblins, bugbears, or drow are gone through in 10 rounds.

Also, if you don't have the libraries then you can put this at the top of your code:

#list of packages
listOfPackages <- c('dplyr',      #data munging
                    'ggplot2',    #nice plotting
                    'psych')

#if not installed, then install and import
for (i in 1:length(listOfPackages)){
  if(!listOfPackages[i] %in% installed.packages(fields = "Package")){
    install.packages(listOfPackages[i] , dependencies = TRUE)
  }
  require(package = listOfPackages[i], character.only = T, quietly = T)
}
rm(i, listOfPackages)
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    \$\begingroup\$ Why are you using proficiency of +6? That's only for a character of level 17 through 20. Most play does not happen at that level. (Beyond that loved your answer and the fact that you showed your work). \$\endgroup\$ – KorvinStarmast Jan 6 at 20:14
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    \$\begingroup\$ Also log$hit is a hilariously unfortunate variable name \$\endgroup\$ – Ifusaso Jan 6 at 20:15
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    \$\begingroup\$ I'm a little unclear what the exact results are without digging through the actual numbers. Could you add a summary section to the top or bottom? Also, I couldn't tell if you accounted for Advantage with the indicated information \$\endgroup\$ – Ifusaso Jan 6 at 20:22
  • 1
    \$\begingroup\$ I don't know much about this language, but couldn't you modify the code or do multiple snippets to show the increasing nature of proficiency? A different possible solution would be to build into your assumption that enemy AC grew at the same rate as your proficiency bonus, so you could safely ignore it. Would fit better than assuming a lv 1 thorough to lv 16 had a lv 17+'s proficiency bonus. \$\endgroup\$ – Joe D. Jan 7 at 6:33

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